Staggered explicit-implicit time-discretization for elastodynamics with dissipative internal variables

An extension of the two-step staggered time discretization linear elastodynamics in stress-velocity form to systems involving internal variables subjected a possibly non-linear dissipative evolution is proposed. The original scheme thus enhanced by another step for which, general, implicit, although even this might be explicit if no spatial gradients are involved. Using an abstract Banach-space formulation, priori estimates and convergence proved under CFL condition. developed three-step finds applications various problems continuum mechanics at small strain. Here, we consider particular plasticity, viscoelasticity (creep), diffusion poroelastic media, damage.